Question

Two large black plane surfaces are maintained at constant temperatures $T_1$ and $T_2(T_1>T_2)$. Two thin black plates $A$ and $B$ are placed between the two surfaces and in parallel to the given plates. After some time, steady conditions are obtained. By what factor, is the steady heat flow increased due to the removal of black plates?

Answer 1

Let the temperatures of $A$ and $B$ be $T_3$ and $T_4$.
Using Stefan-Boltzmann Law
In the steady state,
$Q=\sigma (T_1^4-T_3^4)=\sigma (T_3^4-T_4^4)=\sigma (T_4^2-T_2^2)$
In the absence of plates,
$Q_0=\sigma (T_1^4-T_2^4)=\sigma (T_1^4-T_3^4)+\sigma (T_3^4-T_4^4)+\sigma (T_4^2-T_2^2)\Rightarrow Q_0=3Q$